Streaming Instabilities in Relativistic Magnetoplasmas

Abstract

Stability of superluminous and subluminous waves propagating transverse to the direction of the external uniform magnetic field is investigated in streaming relativistic homogeneous plasmas. In the relativistic regime for $\ensuremath{\Omega}<\mathrm{ck}$ ($\ensuremath{\Omega}$ being the electron cyclotron frequency and $k$ the characteristic wave number), the superluminous waves remain stable as in the absence of external magnetic field; however, for the subluminous waves, the magnetic field has a tendency towards destabilization. For $\ensuremath{\Omega}\ensuremath{\gg}\mathrm{ck}$, the superlum inous waves are dynamically unstable for all streaming velocities $U$, which are smaller than ${U}_{c}$, or for magnetic fields $\ensuremath{\Omega}$, which are greater than ${\ensuremath{\Omega}}_{c}$, but for the waves with frequencies $\ensuremath{\omega}\ensuremath{\ll}\ensuremath{\Omega}$ ($\ensuremath{\Omega}\ensuremath{\gg}\mathrm{ck}$), there exists a minimum streaming velocity above which the system is unstable. In the nonrelativistic regime the system is unstable if streaming is much larger than the thermal velocity but otherwise stable. The unstable region is bounded by ${\ensuremath{\Omega}}_{min}$ and ${\ensuremath{\Omega}}_{max}$; ${\ensuremath{\Omega}}_{min}$ being $k{v}_{t}$ (${v}_{t}$ being the electron thermal velocity) and ${\ensuremath{\Omega}}_{max}$ being $\mathrm{kU}$.